Equilateral Area

Level pending

There is an equilateral triangle \(ABC\) with points \(D\), \(E\) and \(F\) on lines \(AB\), \(BC\) and \(CA\) respectively.

\(AD = 2BD\), \(BE = 2CE\) and \(CF = 2AF\). If \(D\), \(E\) and \(F\) are connected to form a triangle and the side lengths of \(ABC\) are 62 each, what is the area of \(DEF\) to the nearest integer?

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